Subgroups — C₅₉×#33533 #28445642

Order 15104.

1102 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3584	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₉×#3414	C₂	1	2	yes	maximal, complemented
3	C₅₉×#3060	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2191	C₂	1	4	yes	maximal, complemented
5	C₅₉×#2190	C₂	1	4	yes	maximal, complemented
6	C₂×C₅₉×#360	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2115	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#585	—	2	1	no	—
9	C₅₉×#578	—	2	2	no	—
10	C₅₉×#577	—	2	4	no	—
11	C₅₉×#576	—	2	2	no	—
12	C₅₉×#575	—	2	1	no	—
13	C₅₉×#575	C₂²	1	4	yes	—
14	C₂×#135×C₅₉	—	2	2	no	—
15	C₂×#135×C₅₉	C₂²	1	2	yes	—
16	C₂×#135×C₅₉	C₂²	1	1	yes	characteristic, complemented
17	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
18	C₅₉×#537	—	2	1	no	—
19	C₅₉×#510	—	2	2	no	—
20	C₅₉×#510	C₂²	1	4	yes	complemented
21	C₅₉×#509	—	2	2	no	—
22	C₅₉×#509	C₂²	1	4	yes	complemented
23	C₅₉×#508	—	2	4	no	—
24	C₂×M₃₂×C₅₉	C₂²	1	2	yes	complemented
25	C₅₉×#470	C₂²	1	2	yes	complemented
26	C₅₉×#469	C₂²	1	2	yes	complemented
27	C₅₉×#465	—	2	2	no	—
28	C₂×#106×C₅₉	C₂²	1	1	yes	characteristic, complemented
29	C₅₉×#417	—	2	1	no	—
30	C₅₉×#360	C₂²	1	8	yes	complemented
31	C₅₉×#349	C₂²	1	4	yes	complemented
32	2₋¹⁺⁴×C₅₉	—	2	4	no	—
33	2₋¹⁺⁴×C₅₉	—	4	1	no	—
34	H(5,𝔽₂)×C₅₉	—	2	4	no	—
35	H(5,𝔽₂)×C₅₉	—	4	2	no	—
36	H(5,𝔽₂)×C₅₉	—	4	1	no	—
37	C₂×#41×C₅₉	—	2	4	no	—
38	C₂×#41×C₅₉	—	2	2	no	—
39	C₂×#41×C₅₉	—	2	1	no	—
40	C₂×#41×C₅₉	—	4	4	no	—
41	C₂×#41×C₅₉	D₄	1	1	yes	characteristic
42	#137×C₅₉	—	2	4	no	—
43	#137×C₅₉	—	2	8	no	—
44	AGL(1,ℤ/8)×C₅₉	—	2	4	no	—
45	AGL(1,ℤ/8)×C₅₉	—	2	8	no	—
46	#135×C₅₉	—	2	4	no	—
47	#135×C₅₉	—	2	4	no	—
48	#135×C₅₉	—	2	2	no	—
49	#135×C₅₉	—	2	4	no	—
50	#135×C₅₉	—	2	2	no	—
51	#135×C₅₉	—	2	2	no	—
52	#135×C₅₉	—	2	2	no	—
53	#135×C₅₉	D₄	1	4	yes	complemented
54	#135×C₅₉	C₂³	1	4	yes	—
55	C₂×Q₁₆×C₅₉	—	2	2	no	—
56	C₂×Q₁₆×C₅₉	D₄	1	2	yes	complemented
57	C₂×Q₁₆×C₅₉	C₂³	1	1	yes	characteristic
58	C₂×SD₁₆×C₅₉	—	2	4	no	—
59	C₂×SD₁₆×C₅₉	—	2	2	no	—
60	C₂×SD₁₆×C₅₉	—	2	1	no	—
61	C₂×D₈×C₅₉	—	2	2	no	—
62	C₂×D₈×C₅₉	D₄	1	2	yes	complemented
63	C₂×D₈×C₅₉	C₂³	1	1	yes	characteristic
64	#131×C₅₉	—	2	2	no	—
65	#131×C₅₉	—	2	2	no	—
66	C₂×M₁₆×C₅₉	D₄	1	1	yes	characteristic
67	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
68	C₂²×C₈×C₅₉	D₄	1	2	yes	—
69	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
70	C₂²⋊Q₈×C₅₉	—	2	2	no	—
71	C₂²⋊Q₈×C₅₉	—	4	1	no	—
72	#121×C₅₉	—	2	2	no	—
73	#121×C₅₉	—	4	1	no	—
74	#121×C₅₉	—	4	2	no	—
75	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
76	Q₃₂×C₅₉	—	2	4	no	—
77	SD₃₂×C₅₉	—	2	4	no	—
78	SD₃₂×C₅₉	—	2	4	no	—
79	D₁₆×C₅₉	—	2	4	no	—
80	M₃₂×C₅₉	—	2	2	no	—
81	M₃₂×C₅₉	C₂³	1	4	yes	—
82	C₂×C₁₆×C₅₉	—	2	2	no	—
83	#106×C₅₉	—	2	1	no	—
84	#106×C₅₉	C₂³	1	2	yes	—
85	#103×C₅₉	—	2	2	no	—
86	#102×C₅₉	—	2	2	no	—
87	#41×C₅₉	—	2	2	no	—
88	#41×C₅₉	—	2	2	no	—
89	#41×C₅₉	—	2	8	no	—
90	#41×C₅₉	—	2	4	no	—
91	#41×C₅₉	—	2	4	no	—
92	#41×C₅₉	—	4	4	no	—
93	#41×C₅₉	—	4	8	no	—
94	#41×C₅₉	—	4	4	no	—
95	#41×C₅₉	—	4	4	no	—
96	#41×C₅₉	—	4	4	no	—
97	#41×C₅₉	—	4	2	no	—
98	#41×C₅₉	—	4	2	no	—
99	#41×C₅₉	—	4	2	no	—
100	#41×C₅₉	—	4	2	no	—
101	C₂×Q₈×C₅₉	—	2	4	no	—
102	C₂×Q₈×C₅₉	—	2	2	no	—
103	C₂×Q₈×C₅₉	—	2	1	no	—
104	C₂×Q₈×C₅₉	—	4	4	no	—
105	C₂×Q₈×C₅₉	D₈	1	1	yes	characteristic
106	C₂×D₄×C₅₉	—	2	4	no	—
107	C₂×D₄×C₅₉	—	2	2	no	—
108	C₂×D₄×C₅₉	—	2	1	no	—
109	C₂×D₄×C₅₉	—	4	8	no	—
110	C₂×D₄×C₅₉	—	4	4	no	—
111	C₂×D₄×C₅₉	—	4	4	no	—
112	C₂×D₄×C₅₉	—	4	2	no	—
113	C₂×D₄×C₅₉	—	4	1	no	—
114	C₂×D₄×C₅₉	—	4	2	no	—
115	C₂×D₄×C₅₉	D₈	1	2	yes	—
116	C₂×D₄×C₅₉	D₈	1	1	yes	characteristic
117	C₂²×C₄×C₅₉	—	4	4	no	—
118	C₂²×C₄×C₅₉	—	4	2	no	—
119	C₂²×C₄×C₅₉	—	4	1	no	—
120	C₂²×C₄×C₅₉	—	4	1	no	—
121	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
123	Q₁₆×C₅₉	—	2	4	no	—
124	Q₁₆×C₅₉	—	2	2	no	—
125	Q₁₆×C₅₉	—	2	2	no	—
126	Q₁₆×C₅₉	C₂×D₄	1	4	yes	—
127	SD₁₆×C₅₉	—	2	8	no	—
128	SD₁₆×C₅₉	—	2	4	no	—
129	SD₁₆×C₅₉	—	2	4	no	—
130	SD₁₆×C₅₉	—	4	1	no	—
131	SD₁₆×C₅₉	—	4	1	no	—
132	D₈×C₅₉	—	2	4	no	—
133	D₈×C₅₉	—	2	2	no	—
134	D₈×C₅₉	—	2	2	no	—
135	D₈×C₅₉	C₂×D₄	1	4	yes	—
136	M₁₆×C₅₉	—	2	2	no	—
137	M₁₆×C₅₉	—	2	4	no	—
138	C₂×C₈×C₅₉	—	2	2	no	—
139	C₂×C₈×C₅₉	—	2	2	no	—
140	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
144	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
145	C₄⋊C₄×C₅₉	—	2	2	no	—
146	C₄⋊C₄×C₅₉	—	4	1	no	—
147	C₄⋊C₄×C₅₉	—	4	2	no	—
148	C₂²⋊C₄×C₅₉	—	4	2	no	—
149	C₂²⋊C₄×C₅₉	—	4	2	no	—
150	C₁₆×C₅₉	—	2	4	no	—
151	C₂³×C₅₉	—	4	4	no	—
152	C₂³×C₅₉	—	4	2	no	—
153	C₂³×C₅₉	—	4	1	no	—
154	C₂³×C₅₉	C₂×D₈	1	2	yes	—
155	C₂³×C₅₉	C₂×D₈	1	1	yes	characteristic
156	Q₈×C₅₉	—	2	2	no	—
157	Q₈×C₅₉	—	2	4	no	—
158	Q₈×C₅₉	—	4	4	no	—
159	Q₈×C₅₉	—	4	2	no	—
160	Q₈×C₅₉	—	4	1	no	—
161	Q₈×C₅₉	—	4	1	no	—
162	D₄×C₅₉	—	2	4	no	—
163	D₄×C₅₉	—	2	4	no	—
164	D₄×C₅₉	—	2	2	no	—
165	D₄×C₅₉	—	4	4	no	—
166	D₄×C₅₉	—	4	8	no	—
167	D₄×C₅₉	—	4	4	no	—
168	D₄×C₅₉	—	4	4	no	—
169	D₄×C₅₉	—	4	1	no	—
170	D₄×C₅₉	—	4	1	no	—
171	D₄×C₅₉	—	4	2	no	—
172	D₄×C₅₉	—	8	2	no	—
173	D₄×C₅₉	—	16	2	no	—
174	C₂×C₄×C₅₉	—	2	2	no	—
175	C₂×C₄×C₅₉	—	2	2	no	—
176	C₂×C₄×C₅₉	—	4	8	no	—
177	C₂×C₄×C₅₉	—	4	4	no	—
178	C₂×C₄×C₅₉	—	4	2	no	—
179	C₂×C₄×C₅₉	—	4	4	no	—
180	C₂×C₄×C₅₉	—	4	4	no	—
181	C₂×C₄×C₅₉	—	4	2	no	—
182	C₂×C₄×C₅₉	—	4	1	no	—
183	C₂×C₄×C₅₉	—	8	2	no	—
184	C₂×C₄×C₅₉	—	16	1	no	—
185	C₂×C₄×C₅₉	#120	1	2	yes	—
186	C₂×C₄×C₅₉	C₂×D₈	1	2	yes	—
187	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
188	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
189	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
190	C₈×C₅₉	—	2	2	no	—
191	C₈×C₅₉	#120	1	1	yes	characteristic
192	C₈×C₅₉	#120	1	1	yes	characteristic
193	C₈×C₅₉	C₂²×D₄	1	2	yes	—
194	#33533	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂²×C₅₉	—	2	2	no	—
196	C₂²×C₅₉	—	4	1	no	—
197	C₂²×C₅₉	—	4	2	no	—
198	C₂²×C₅₉	—	4	4	no	—
199	C₂²×C₅₉	—	8	1	no	—
200	C₂²×C₅₉	—	8	1	no	—
201	C₂²×C₅₉	—	8	1	no	—
202	C₂²×C₅₉	—	16	2	no	—
203	C₂²×C₅₉	—	16	4	no	—
204	C₂²×C₅₉	#447	1	2	yes	—
205	C₂²×C₅₉	C₂²×D₈	1	1	yes	characteristic
206	C₄×C₅₉	—	2	2	no	—
207	C₄×C₅₉	—	4	4	no	—
208	C₄×C₅₉	—	8	2	no	—
209	C₄×C₅₉	—	8	1	no	—
210	C₄×C₅₉	#447	1	2	yes	—
211	C₄×C₅₉	C₂×#120	1	1	yes	characteristic
212	C₄×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
213	#3584	C₂×C₅₉	1	1	yes	characteristic, complemented
214	#3414	C₂×C₅₉	1	2	yes	complemented
215	#3060	C₂×C₅₉	1	1	yes	characteristic, complemented
216	#2191	C₂×C₅₉	1	4	yes	complemented
217	#2190	C₂×C₅₉	1	4	yes	complemented
218	C₂×#360	C₂×C₅₉	1	2	yes	complemented
219	#2115	C₂×C₅₉	1	1	yes	characteristic, complemented
220	C₂×C₅₉	—	2	1	no	—
221	C₂×C₅₉	—	2	2	no	—
222	C₂×C₅₉	—	4	2	no	—
223	C₂×C₅₉	—	8	4	no	—
224	C₂×C₅₉	—	16	1	no	—
225	C₂×C₅₉	C₂×#447	1	1	yes	characteristic
226	#585	—	2	1	no	—
227	#578	—	2	2	no	—
228	#577	—	2	4	no	—
229	#576	—	2	2	no	—
230	#575	—	2	1	no	—
231	#575	C₂²×C₅₉	1	4	yes	—
232	C₂×#135	—	2	2	no	—
233	C₂×#135	C₂²×C₅₉	1	2	yes	—
234	C₂×#135	C₂²×C₅₉	1	1	yes	characteristic, complemented
235	C₂×#131	C₂²×C₅₉	1	1	yes	characteristic
236	#537	—	2	1	no	—
237	#510	—	2	2	no	—
238	#510	C₂²×C₅₉	1	4	yes	complemented
239	#509	—	2	2	no	—
240	#509	C₂²×C₅₉	1	4	yes	complemented
241	#508	—	2	4	no	—
242	C₂×M₃₂	C₂²×C₅₉	1	2	yes	complemented
243	#470	C₂²×C₅₉	1	2	yes	complemented
244	#469	C₂²×C₅₉	1	2	yes	complemented
245	#465	—	2	2	no	—
246	C₂×#106	C₂²×C₅₉	1	1	yes	characteristic, complemented
247	#417	—	2	1	no	—
248	#360	C₂²×C₅₉	1	8	yes	complemented
249	#349	C₂²×C₅₉	1	4	yes	complemented
250	C₅₉	#33533	1	1	yes	characteristic, direct product factor, Sylow
251	2₋¹⁺⁴	—	2	4	no	—
252	2₋¹⁺⁴	—	4	1	no	—
253	H(5,𝔽₂)	—	2	4	no	—
254	H(5,𝔽₂)	—	4	2	no	—
255	H(5,𝔽₂)	—	4	1	no	—
256	C₂×#41	—	2	4	no	—
257	C₂×#41	—	2	2	no	—
258	C₂×#41	—	2	1	no	—
259	C₂×#41	—	4	4	no	—
260	C₂×#41	D₄×C₅₉	1	1	yes	characteristic
261	#137	—	2	4	no	—
262	#137	—	2	8	no	—
263	AGL(1,ℤ/8)	—	2	4	no	—
264	AGL(1,ℤ/8)	—	2	8	no	—
265	#135	—	2	4	no	—
266	#135	—	2	4	no	—
267	#135	—	2	2	no	—
268	#135	—	2	4	no	—
269	#135	—	2	2	no	—
270	#135	—	2	2	no	—
271	#135	—	2	2	no	—
272	#135	D₄×C₅₉	1	4	yes	complemented
273	#135	C₂³×C₅₉	1	4	yes	—
274	C₂×Q₁₆	—	2	2	no	—
275	C₂×Q₁₆	D₄×C₅₉	1	2	yes	complemented
276	C₂×Q₁₆	C₂³×C₅₉	1	1	yes	characteristic
277	C₂×SD₁₆	—	2	4	no	—
278	C₂×SD₁₆	—	2	2	no	—
279	C₂×SD₁₆	—	2	1	no	—
280	C₂×D₈	—	2	2	no	—
281	C₂×D₈	D₄×C₅₉	1	2	yes	complemented
282	C₂×D₈	C₂³×C₅₉	1	1	yes	characteristic
283	#131	—	2	2	no	—
284	#131	—	2	2	no	—
285	C₂×M₁₆	D₄×C₅₉	1	1	yes	characteristic
286	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
287	C₂²×C₈	D₄×C₅₉	1	2	yes	—
288	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
289	C₂²⋊Q₈	—	2	2	no	—
290	C₂²⋊Q₈	—	4	1	no	—
291	#121	—	2	2	no	—
292	#121	—	4	1	no	—
293	#121	—	4	2	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	Q₃₂	—	2	4	no	—
296	SD₃₂	—	2	4	no	—
297	SD₃₂	—	2	4	no	—
298	D₁₆	—	2	4	no	—
299	M₃₂	—	2	2	no	—
300	M₃₂	C₂³×C₅₉	1	4	yes	—
301	C₂×C₁₆	—	2	2	no	—
302	#106	—	2	1	no	—
303	#106	C₂³×C₅₉	1	2	yes	—
304	#103	—	2	2	no	—
305	#102	—	2	2	no	—
306	#41	—	2	2	no	—
307	#41	—	2	2	no	—
308	#41	—	2	8	no	—
309	#41	—	2	4	no	—
310	#41	—	2	4	no	—
311	#41	—	4	4	no	—
312	#41	—	4	8	no	—
313	#41	—	4	4	no	—
314	#41	—	4	4	no	—
315	#41	—	4	4	no	—
316	#41	—	4	2	no	—
317	#41	—	4	2	no	—
318	#41	—	4	2	no	—
319	#41	—	4	2	no	—
320	C₂×Q₈	—	2	4	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	4	4	no	—
324	C₂×Q₈	D₈×C₅₉	1	1	yes	characteristic
325	C₂×D₄	—	2	4	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	4	8	no	—
329	C₂×D₄	—	4	4	no	—
330	C₂×D₄	—	4	4	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂×D₄	—	4	1	no	—
333	C₂×D₄	—	4	2	no	—
334	C₂×D₄	D₈×C₅₉	1	2	yes	—
335	C₂×D₄	D₈×C₅₉	1	1	yes	characteristic
336	C₂²×C₄	—	4	4	no	—
337	C₂²×C₄	—	4	2	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	—	4	1	no	—
340	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
341	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
342	Q₁₆	—	2	4	no	—
343	Q₁₆	—	2	2	no	—
344	Q₁₆	—	2	2	no	—
345	Q₁₆	C₂×D₄×C₅₉	1	4	yes	—
346	SD₁₆	—	2	8	no	—
347	SD₁₆	—	2	4	no	—
348	SD₁₆	—	2	4	no	—
349	SD₁₆	—	4	1	no	—
350	SD₁₆	—	4	1	no	—
351	D₈	—	2	4	no	—
352	D₈	—	2	2	no	—
353	D₈	—	2	2	no	—
354	D₈	C₂×D₄×C₅₉	1	4	yes	—
355	M₁₆	—	2	2	no	—
356	M₁₆	—	2	4	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
360	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
361	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
362	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
363	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	4	1	no	—
366	C₄⋊C₄	—	4	2	no	—
367	C₂²⋊C₄	—	4	2	no	—
368	C₂²⋊C₄	—	4	2	no	—
369	C₁₆	—	2	4	no	—
370	C₂³	—	4	4	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	4	1	no	—
373	C₂³	C₂×D₈×C₅₉	1	2	yes	—
374	C₂³	C₂×D₈×C₅₉	1	1	yes	characteristic
375	Q₈	—	2	2	no	—
376	Q₈	—	2	4	no	—
377	Q₈	—	4	4	no	—
378	Q₈	—	4	2	no	—
379	Q₈	—	4	1	no	—
380	Q₈	—	4	1	no	—
381	D₄	—	2	4	no	—
382	D₄	—	2	2	no	—
383	D₄	—	2	4	no	—
384	D₄	—	4	4	no	—
385	D₄	—	4	8	no	—
386	D₄	—	4	4	no	—
387	D₄	—	4	4	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	1	no	—
390	D₄	—	4	1	no	—
391	D₄	—	8	2	no	—
392	D₄	—	16	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	8	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	—	4	4	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	8	2	no	—
403	C₂×C₄	—	16	1	no	—
404	C₂×C₄	#120×C₅₉	1	2	yes	—
405	C₂×C₄	C₂×D₈×C₅₉	1	2	yes	—
406	C₂×C₄	C₂×D₈×C₅₉	1	1	yes	characteristic
407	C₂×C₄	AGL(1,ℤ/8)×C₅₉	1	2	yes	—
408	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
409	C₈	—	2	2	no	—
410	C₈	#120×C₅₉	1	1	yes	characteristic
411	C₈	#120×C₅₉	1	1	yes	characteristic
412	C₈	C₂²×D₄×C₅₉	1	2	yes	—
413	C₂²	—	2	2	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	4	4	no	—
417	C₂²	—	8	1	no	—
418	C₂²	—	8	1	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	16	2	no	—
421	C₂²	—	16	4	no	—
422	C₂²	C₅₉×#447	1	2	yes	—
423	C₂²	C₂²×D₈×C₅₉	1	1	yes	characteristic
424	C₄	—	2	2	no	—
425	C₄	—	4	4	no	—
426	C₄	—	8	2	no	—
427	C₄	—	8	1	no	—
428	C₄	C₅₉×#447	1	2	yes	—
429	C₄	C₂×#120×C₅₉	1	1	yes	characteristic
430	C₄	C₂×AGL(1,ℤ/8)×C₅₉	1	1	yes	characteristic
431	C₂	—	2	1	no	—
432	C₂	—	2	2	no	—
433	C₂	—	4	2	no	—
434	C₂	—	8	4	no	—
435	C₂	—	16	1	no	—
436	C₂	C₂×C₅₉×#447	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅₉	C₂×#447
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅₉
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ C₂×#131×C₅₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅₉×#3584	C₂	semidirect
2. C₅₉×#3414	C₂	semidirect
3. C₅₉×#3060	C₂	semidirect
4. C₅₉×#2191	C₂	semidirect
5. C₅₉×#2190	C₂	semidirect
6. C₂×C₅₉×#360	C₂	semidirect
7. C₅₉×#2115	C₂	semidirect
16. C₂×#135×C₅₉	C₂²	semidirect
20. C₅₉×#510	C₂²	semidirect
22. C₅₉×#509	C₂²	semidirect
24. C₂×M₃₂×C₅₉	C₂²	semidirect
25. C₅₉×#470	C₂²	semidirect
26. C₅₉×#469	C₂²	semidirect
28. C₂×#106×C₅₉	C₂²	semidirect
30. C₅₉×#360	C₂²	semidirect
31. C₅₉×#349	C₂²	semidirect
53. #135×C₅₉	D₄	semidirect
56. C₂×Q₁₆×C₅₉	D₄	semidirect
62. C₂×D₈×C₅₉	D₄	semidirect
194. #33533	C₅₉	direct (N × H)
213. #3584	C₂×C₅₉	semidirect
214. #3414	C₂×C₅₉	semidirect
215. #3060	C₂×C₅₉	semidirect
216. #2191	C₂×C₅₉	semidirect
217. #2190	C₂×C₅₉	semidirect
218. C₂×#360	C₂×C₅₉	semidirect
219. #2115	C₂×C₅₉	semidirect
234. C₂×#135	C₂²×C₅₉	semidirect
238. #510	C₂²×C₅₉	semidirect
240. #509	C₂²×C₅₉	semidirect
242. C₂×M₃₂	C₂²×C₅₉	semidirect
243. #470	C₂²×C₅₉	semidirect
244. #469	C₂²×C₅₉	semidirect
246. C₂×#106	C₂²×C₅₉	semidirect
248. #360	C₂²×C₅₉	semidirect
249. #349	C₂²×C₅₉	semidirect
250. C₅₉	#33533	direct (N × H)
272. #135	D₄×C₅₉	semidirect
275. C₂×Q₁₆	D₄×C₅₉	semidirect
281. C₂×D₈	D₄×C₅₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅₉×#3584	2
C₅₉×#3414	2
C₅₉×#3060	2
C₅₉×#2191	2
C₅₉×#2190	2
C₂×C₅₉×#360	2
C₅₉×#2115	2
#33533	59

Subgroups — C59×#33533 #28445642

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#33533 #28445642